Yes, I'd suggest a book on special relativity before tackling Hartle, though Hartle does cover SR. If you're finding that section of his book difficult, I'd suggest, as usual, the red paperback first edition of Spacetime Physics.

You should definitely have had some exposure to SR before going through Hartle's Gravity. Even exposure on the level of simply manipulating lorentz factors and whatnot is very helpful before presented with the 4-vector formulation of everything. The book is, after all, an introduction to general relativity, and just quickly glosses over stuff from SR as a refresher/analogy to GR.